Simple undivided plane UV map not behaving as expected
A face is always composed of 2 triangles, the oblique goes in a sense or in the other:

so if you give your face an image texture then deform the face by moving its vertices, the result may be unexpected deformations like this:

You have several solutions like creating directly the final quad shape instead of deforming a square face, or subdivide enough your square so that the deformation becomes not noticeable.